50 
MR. LUBBOCK’S RESEARCHES 
9a = 
+ r «7 Js '“ - 2 ^*- - 4 J »,- + 4 $ { (‘ + $) - 2 ^ *>.. - £*m } 
3 a . 3 a , 
O q "1 0 0 ‘1,0 
2 a, 9 2 a? 
a 2 
- — &, , 
£-6. 
2 a, 3 3,1 
4 a/ 2 • 
3 ti j 3 ci j 
2a? + ~2 a? 3 ’ ( 
2 a 2 j 
1 2a 3 3> 
a 
1 4 a/ 2 1 
3^ a 2 
2 a,, 
_2 a~ 
4 a/ 2 
The quantities of which the general symbol is q, and which refer to the 
terms in the development of R multiplied by the eccentricities, admit of similar 
reductions ; so that 
u~ i a 7 
?7 — — Tl 6 3,0 + -1 6 3,1 
a 7 a. 1 
9 16 — — 
a , 
2 a/ 2 3,2 
Considering only the terms in 2 J'dR + r ( w ^ich the arguments are 
»* + e — •ur, and n t -{- s — ht / 
2 / dR + r ft?) = m, q 1 e cos (nt + s — -us) + m i q l6 e, cos (n t + s — or,) 
= wq q cos (n t + s — •sr 1 ) 
provided 
And if 
q cos r ns x —q 1 e cos ot + q x6 e t cos sq 
q cos ra-j = q 1 e sin -us + q x6 e t sin r m i 
— 1 + r 0 + e cos (n (1 4- k) t + s — sr.j + &c. 
(1 +fc)«(l -3r 0 )- 1 + ^q=0 
/x e 
.3 m, a 
k = Y r °-^ 
r 0 = -‘ 1— 6 3 0 -J-b 31 ) 
0 fa la, 3 3,0 2 a, 2 3,1 / 
q 5 = Vi* e- + 2 q. q l6 e e, cos (ot — ®q) + g 16 2 e,® 
q = ?? e + ?io e i cos O — w) nearly 
Q Q>~ j . CL j CL 6 1 j / \ 
— = - — 3 ho + — o *3,1 - o~ 1 i — ^V-C 0 * 5 - OT /) 
e a 3 af ’ 2 a, 2 e 
, m. f 3 a 3 7 3 a 2 , . a 3 , a 2 , , a 1 , c, , >1 
/X 1 2 a, 3 3,0 4 a, 2 3,1 2 a, 3 3,0 2 a/ 2 3,1 4 a/ 2 3,2 e v " J 
m, f 2 a 3 , 5 a 2 , , a 2 , e, , % "I 
/X l a, 3 3,0 4 a, 2 3,1 4 a/ 2 3,2 e v "j 
